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A tractor yes, especially with PTO and constant towing.

But a backhoe? 57 HP continuously just to swing the buckets?

Is a backhoe harder duty than what an active forklift does? Now a forklift has a pump motor in addition to the traction motor, but I think it also moves faster (it's also only 2/3 the weight).

Just spitballing here.
You are forgetting the loader bucket at the other end of the hoe. You will need all of that HP(sometimes you wish you had more!) to dig and push into undisturbed dirt or piles of dirt, crushed rock, and other materials that need to be lifted up and moved around.
This might be a case where multiple smaller motors running in parallel would provide enough power. For batteries you might look into new or used forklift batteries: forklift batteries for sale - Google Shopping
There is quite an extensive market for these batteries. Some of them are designed to be swapped-out and recharged between work shifts
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